Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-57232008-542702120090401WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS107131ENAllaberenAshyralyevDepartment of Mathematics, Fatih University, Istanbul,34500, Turkeyaashyralyev@fatih.edu.trAyferDuralGaziosman Paşa Lisesi Istanbul, TurkeyYaşarSözenDepartment of Mathematics, Fatih University, Istanbul,34500, Turkeyysozen@fatih.edu.trhttp://ijo.iaurasht.ac.ir/article_513242.htmlhttp://ijo.iaurasht.ac.ir/article_513242_b696c46c223d5893189894ebd386e2a2.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-57232008-542702120090701A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA132140ENVictorA.PlotnikovDepartment of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, UkraineOlgaD.KichmarenkoDepartment of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraineolga.kichmarenko@gmail.com<span>Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.</span>averaging method,DIFFERENTIAL EQUATIONS WITH DELAY,DIFFERENTIAL EQUATIONS WITH MAXIMA,AUTOMATIC REGULATIONhttp://ijo.iaurasht.ac.ir/article_513243.htmlhttp://ijo.iaurasht.ac.ir/article_513243_5f3c8ae8ea9dc142b1dc6d4d96b4a7fb.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-57232008-542702120090701COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM141150ENA. R.VahidiDepartment of Mathematics, Shahr-e-Rey Branch, Islamic Azad Universityalrevahidi@yahoo.comGH.Asadi CordshooliDepartment of Physics, Shahr-e-Rey Branch, Islamic Azad UniversityZ.AzimzadehDepartment of Mathematics, Science and Research Branch, Islamic Azad University<span>In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply. </span>Adomian decomposition method,Differential equation,damped forced oscillatorhttp://ijo.iaurasht.ac.ir/article_513244.htmlhttp://ijo.iaurasht.ac.ir/article_513244_30c8e012f97a5925f518417591ecc74f.pdfIslamic Azad University, Rasht BranchIranian Journal of Optimization2588-57232008-542702120090701INTEGRATING CASE-BASED REASONING, KNOWLEDGE-BASED APPROACH AND TSP ALGORITHM FOR MINIMUM TOUR FINDING151161ENHosseinErfaniDepartment of computer Lahijan I.A.U.herfani@gmail.com<span>Imagine you have traveled to an unfamiliar city. Before you start your daily tour around the city, you need to know a good route. In Network Theory (NT), this is the traveling salesman problem (TSP). A dynamic programming algorithm is often used for solving this problem. However, when the road network of the city is very complicated and dense, which is usually the case, it will take too long for the algorithm to find the shortest path. Furthermore, in reality, things are not as simple as those stated in AT. For instance, the cost of travel for the same part of the city at different times may not be the same. In this project, we have integrated TSP algorithm with AI knowledge-based approach and case-based reasoning in solving the problem. With this integration, knowledge about the geographical information and past cases are used to help TSP algorithm in finding a solution. This approach dramatically reduces the computation time required for minimum tour finding.</span>CASE-BASED REASONING,KNOWLEDGE-BASED APPROACH,Traveling salesman problem,CASE-BASED TOUR FINDER,KNOWLEDGE-BASED ROUTE FINDER,Geographical Informationhttp://ijo.iaurasht.ac.ir/article_513245.htmlhttp://ijo.iaurasht.ac.ir/article_513245_3c4d2bff5986f79d2b7094d0cd0a9317.pdf